Weekly CI job to update Manifest and post a PR

[penelopeysm]

Every time I write new docs or update stuff, I run into weird stuff happening with deps, whether it's SciML stuff or ForwardDiff 1.0 or just other weird things. This time (#676), it's the Core Functionality page which broke, which is a bit ironic.

I think it would make sense to have a weekly cron job that runs Pkg.update() in the top level dir and makes a PR with any changes to Manifest.toml, then at least we can separate the task of writing docs from the task of keeping up to date with dependency churn.

[penelopeysm]

I hate to do this, but @copilot maybe this is one for you

[penelopeysm]

... on second thoughts, I hate these AI things so much, I'll do it myself